Combining Like Terms with the Distributive Property

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Objective

SWBAT apply the distributive property to combining like terms.

Big Idea

How can we clear parentheses to simplify an expression?

Do Now

10 minutes

In a previous lesson, Combining Like Terms, students identified like terms and developed steps for simplifying algebraic expressions.  The Do Now is an assessment of their understanding of like terms.  Problems 2 and 3 display common mistakes made by students.  It is important for students to be able to explain why these are not correct equations.  

Do Now

True or False.  If false, explain why.

1.  8x + 3x = 11x

2.  7x + 7y = 14xy

3.  4x + 4x = 8x2

Simplify

4.  8a + 2 + 3b + 9 + a + 6b + 1

 

 

Mini Lesson

15 minutes

 

This lesson is a continuation of Combining Like Terms, but I will introduce students to how the distributive property can be used to simplify expressions and combine like terms.

We will work through several problems together

Ex. 1 - Simplify 7x + 3(x+ 4)

What property of math do you see in this expression?

Students should recognize that the distributive property can be applied.

How can we simplify this expression using the distributive property?

Students have prior knowledge of the distributive property, but I will review how 3 should be multiplied by both terms in the parentheses.

Can we simplify this expression further? Are there like terms in this expression?

Students should identify 7x and 3x as like terms.

 

Ex. 2 - Simplify 8 + 5(3x + 4y + 2) + 6y

What should we do first?

Students should suggest that we apply the distributive property.  For students who think that we can combine like terms first, I will bring to their attention that, similar to order of operations, we need to clear the parentheses first. 

How many terms are inside the parentheses? What is the 5 distributed to?

Students should know that there are 3 terms that the 5 should be distributed to.

Can we simplify this expression?  Are there like terms?

Students should recognize that they can combine the y variables and the constants.

Ex. 3 - Write an expression for the perimeter of a rectangle with a length of 2x + 4 and a width of x + 9

I will have students draw a rectangle and label it, so it is easier to visualize the problem.

There are two different ways to find the perimeter of a rectangle.  What is one strategy?

Most students will suggest adding all the sides, which will give us the expression 2x + 4 + x + 9 + 2x + 4 + x + 9.  

Can we simplify this expression?

Students should recognize the like terms.  I will remind students to be aware of the "invisible" ones, which changes x to 1x.

What is another strategy for finding perimeter of a rectangle?

Some students may know of the formula P = 2l + 2w.  This will give us the expression 2(2x+4) + 2(x+9).  We will simplify this expression using the distributive property and combining like terms.  It is important for students to see that either method gives us the same simplified expression.

 

Independent Practice

20 minutes

For the Independent Practice, students will be given problems where they will have to apply the distributive property and combining like terms.   

Independent Practice

1) Simplify 4 + (x + 3)6

2)  Simplify 3x2 + 7x + 5(x + 3) + x2

3)  Simplify 9x3 + 2x2 + 3(x2 + x) + 5x

4)  Find the perimeter of a triangle with sides 2x + 3, 5x + 8 + x, and 7x - 2.

5)  Simplify 2(a + 5) - a + 6

6)  Simplify  6y + 4m + 3(3y + m)

7)  Simplify  15 + 2(x + 4) + 10

After 10 minutes, I will assign each group a problem and give them a white board to show their work on.  They will have about 5 minutes to agree on their work and answer with their group, before they present the problem to the class.  Students should be able to explain their work using math vocabulary such as expressions, distributive property, combining like terms, coefficient, constant, and variable.

Exit Ticket

5 minutes

To assess students understanding of combining like terms using the distributive property, I will give them an exit ticket.  The exit ticket will be a problem that will challenge students and force them to carefully organize their work.

 

Exit Ticket

Simplify the expression.

4(x + 5 + 2y) + 4(5y + 6) + (3 + 2x + 8) - 1 + 2(3x + y + 1)

 

I will use the results of the exit ticket to group students for the following lesson.